Description of the Related Art
Discussion of the Problem to be Solved
Owing to the rapidly increasing demands for high capacity and performance of hard disk drives from industry, servo engineers are required to develop more advanced control strategies. It is projected that the position accuracy of hard disk drives will reach 25,000 tracks per inch (TPI) (less than 1 μm per track) at the end of this century. (See, for example, K. K. Chew, Control system challenges to high track density magnetic disk storage, IEEE Transactions on Magnetics, Vol. 32, 1996, pages 1799-1804.) For a system with such a high accuracy requirement, some nonlinearities currently being neglected or simplified in control system design must be taken into account and reconsidered. The nonlinearities preventing the system accuracy of a hard disk drive from further improvement include the ribbon flexibility, the windage, and the nonlinear friction of the actuator pivot of a hard disk drive.
Friction depends on many factors such as the asperity of contact surfaces, lubrication, velocity, temperature, the force orthogonal to the relative motion, and even the history of motion. Friction is a natural phenomenon that is very hard, if not impossible, to model and that has not yet been completely understood. Friction is generally considered having two different manifestations, i.e., the pre-sliding friction and the sliding friction. (See, for example, B. Armstrong-Hélouvry, P. Dupont and C. Canudas de Wit, A survey of models, analysis tools and compensation methods for control of machines with friction, Automatica, Vol. 30, No. 7, 1994, pages 1083-1138.) In the pre-sliding stage, which is usually in the range of less than 10−5 meters, friction is dominated by the elasticity of the contacting asperity of surfaces. Friction not only depends on both position and velocity of motion, but also exhibits nonlinear dynamic behavior such as hysteresis characteristics with respect to position and velocity as observed by many researchers. (See, for example, B. Armstrong-Hélouvry, et al, A survey of models, analysis tools and compensation methods for control of machines with friction, cited above; D. Abramovitch, F. Wang and G. Franklin, Disk drive pivot nonlinearity modeling part I: frequency domain, Proceedings of the American Control Conference, Baltimore, Md., June 1994, pages 2600-2603; F. Wang, T. Hust, D. Abramovitch and G. Franklin, Disk drive pivot nonlinearity modeling part II: time domain, Proceedings of the American Control Conference, Baltimore, Md., June 1994, pages 2604-2607; K. Eddy and W. Messner, Dynamics affecting tracking bias in hard disk drive rotary actuators, Proceedings of the American Control Conference, Seattle, Wash., June 1995, pp. 1055-1060; and C. Canudas de Wit, H. Olsson, K. J. {dot over (A)}strom and P. Lischinsky, A new model for control of systems with friction, IEEE Transactions on Automatic Control, Vol. 40, No. 3, 1995, pages 419-25.) In the sliding stage, friction is dominated by the lubrication of the contacting surfaces and introduces damping into the system. Friction in the sliding stage is usually represented by various functions of velocity.
The problem associated with friction in hard disk drives has been observed widely by manufacturers. Recently, friction has received more attention due to the new challenges for the high density mass storage techniques in the near future (See, for example, B. Armstrong-Hélouvry, et al, A survey of models, analysis tools and compensation methods for control of machines with friction, cited above; D. Abramovitch, et al., Disk drive pivot nonlinearity modeling part I: frequency domain, cited above; and F. Wang, et al., Disk drive pivot nonlinearity modeling part II: time domain, cited above.) The problems due to friction in hard disk drives are summarized as follows:                Nonlinear friction lowers system gain in the low frequency range. It has been observed experimentally that the open-loop low frequency gain decreases as the input amplitude decreases, while the cut-off frequency increases as the input amplitude decreases, as shown in FIG. 1(a) and FIG. 1(b). (See, for example, K. Takaishi, T. Imamura, Y. Mizoshita, S. Hasegawa, T. Ueno and T. Yamada, Microactuator control for Disk Drive, IEEE Transactions on Magnetics, Vol. 32, No. 3, May 1996, pages 1863-1866.)        Friction is a dynamic and nonlinear phenomenon, which depends on many factors including the asperity of contact surfaces, lubrication, velocity, temperature, the force orthogonal to the relative motion, and even the history of motion.        Friction exhibits hysteresis characteristics with respect to both position and velocity.        Due to the nonlinearity and complexity of friction, it is very difficult, if not impossible, to obtain a true friction model.        
For a hard disk drive with positioning accuracy in the micrometer range or higher, friction dynamics in the pre-sliding stage cannot be neglected in control system design. Friction can cause many undesired effects such as steady state errors, tracking lag, and limit cycles in a servo system. For HDD control, one of the important tasks during the track following stage is to reduce the steady state error for improved positioning accuracy because friction reduces system gain in the low frequency range. In view of the difficulty in obtaining a true friction model, a non-model based robust friction compensation method and its variations for implementation are introduced in the present invention, as will be discussed below. To break the restrictions inherent in the traditional Proximate Time-Optimal Servomechanism (PTOS), a triple-mode control scheme and its variations are presented, which introduce extra degrees of freedom in controller design and at the same time, guarantee the continuity of the control signals.
Discussion of Previous Solutions
The positioning control system of the read/write head of a hard disk drive has two tasks: (a) track seeking and (b) track following. In the track seeking stage, the head is forced to move to the target track as quickly as possible. In the track following stage, the head is positioned precisely at the target track.
Integral Control and Observer-based Bias Compensation
The Proximate Time-Optimal Servomechanism (PTOS) is widely employed in the disk drive industry. (See, for example, G. F. Franklin, J. D. Powell and M. L. Workman, Digital Control of Dynamic Systems, Second Edition, Addision-Wesley, 1990.) In a PTOS, the controller switches between two modes: a Proximate Time-Optimal Controller (PTOC) mode for fast seeking when the position error is large, and a linear proportional derivative (PD) controller mode for track following when the position error is within a predefined threshold. Because friction limits the system gain in the low frequency range, the PTOS cannot satisfy the high precision requirement for the new generation of hard disk drives. To solve this problem, the commonly used techniques are (1) integral control and (2) observer-based compensation. (See, for example, G. F. Franklin, et al., Digital Control of Dynamic Systems, cited above.) However, it is well known that an integral control in the positioning system with friction leads to limit cycles. (See, for example, B. Armstrong-Hélouvry, et al, A survey of models, analysis tools and compensation methods for control of machines with friction, cited above; and B. Armstrong and B. Amin, PID control in the presence of static friction: a comparison of algebraic and describing function analysis, Automatica, Vol. 32, No. 5, 1996, pages 679-692.) The observer-based compensation technique was derived under the assumption that the disturbance is a constant bias such that the derivative of the disturbance with respect to time is zero. Unfortunately, in the micrometer level, the dynamics of friction cannot be neglected.
Model-based Friction Compensation
If an accurate friction model can be obtained, a feedforward path can remove the influence of friction. Therefore, suitable friction models for controller design were investigated. (See, for example, D. Abramovitch, et al., Disk drive pivot nonlinearity modeling part I: frequency domain, cited above; F. Wang, et al., Disk drive pivot nonlinearity modeling part II: time domain, cited above; and K. Eddy, et al., Dynamics affecting tracking bias in hard disk drive rotary actuators, cited above.) However, because friction is a complex physical phenomenon which depends on many factors such as the asperity of the contacted surfaces, the situation of lubrication and the temperature, it is difficult to obtain a true model to describe all the physical behaviors of friction. It was found that friction models obtained cannot describe the system behaviors in both frequency and time domains simultaneously. (See, for example, F. Wang, et al., Disk drive pivot nonlinearity modeling part II: time domain, cited above; and K. Eddy, et al., Dynamics affecting tracking bias in hard disk drive rotary actuators, cited above.)
Non-model Based Friction Compensation
Since it is very difficult to obtain a complete friction model, non-model based schemes have been explored. Non-model based compensation schemes can be classified into (1) robust methods and (2) adaptive and learning methods. The usually complicated adaptive and learning methods are not considered to be suitable for the control system of disk drives, which are preferred to be small, simple, compact, reliable and economical. Robust friction compensation has been investigated based on the property of static friction. (See, for example, S. C. Southward, C. J. Radeliff and C. R. MacCluer, Robust nonlinear stick-slip friction compensation, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 113, 1991, pages 639-645. This property does not hold for dynamic friction, which exhibits hysteretic characteristics with respect to both velocity and position.
In summary, a robust, simple and practical solution which can compensate for the effects of friction for hard disk drives is needed.